14 Feb 2006C4: Coronal Energy Inputs I. Mapping Free Energy in
the Solar Atmosphere What can we learn from HMI & AIA? Brian
Welsch, Space Sciences Lab, UC Berkeley What kinds of observations
are required to compute and understand the creation and dissipation
of free energy? How can we best make use of the joint AIA and HMI
dataset? What jobs need to get done before launch to allow proper
analysis and use of the SDO data? This last point, in particular,
is the focus of this session; consequently, my talk is meant to
engender discussion!
Slide 2
14 Feb 2006C4: Coronal Energy Inputs I. Free energy U (F) is
the actual magnetic energy minus the potential magnetic energy. 8 U
(F) = dV [ (B B) - (B (P) B (P) )] Both B(x 1,x 2,x 3 ) and B (P)
(x 1,x 2,x 3 ) match the dist- ribution of normal flux, B n (x 1,x
2 ), at coronas base. Nonpotential part of field is B (x 1,x 2,x 3
) = B - B (P) B (P) carries no currents, or, equivalently, is curl
free. 1.For any B n | S, B (P) has minimal energy. 2. B (P) = - ,
with 2 Laplaces eqn. gives B (P) 3.For any B n | S, B (P) is
unique.
Slide 3
14 Feb 2006C4: Coronal Energy Inputs I. The Free Energy Release
Paradigm motivates studying free magnetic energy (cf.,
earthquakes). 1.Slow photospheric motions (v ~ 1 km/s) add magnetic
energy to the coronal field, as E x B Poynting flux. 2.The
frozen-in flux condition prevents relaxation B B (P), so free
energy is stored in the corona latency. 3.With enough free energy,
the corona reaches an unstable configuration (??) and spontaneously
relaxes toward B (P). Most CME models flux cancellation, breakout,
tether cutting, kink instability accord with this picture. (But
cf., free energy injection paradigm of Chen [1996]).
Slide 4
14 Feb 2006C4: Coronal Energy Inputs I. HMI data can be used in
several ways to quantify free magnetic energy. 1.Use B(x 1,x 2,0)
to extrapolate B & B (P) (McTiernan, Thurs. a.m.) can compare
model fields to AIA data 2.Magnetic Virial Theorem (Wheatland &
Metcalf 2005) novel application to photospheric magnetograms 3.Free
Energy Flux (FEF) through photosphere (Welsch, 2006) gives
photospheric loci of energy injection 4.Magnetic charge topology
(MCT, e.g., Barnes et al. 2005). can give coronal loci of
departures from potential field
Slide 5
14 Feb 2006C4: Coronal Energy Inputs I. 1) Using B(x 1,x 2,0)
from HMI, extrapolations give B(x 1,x 2,x 3 ), allowing integration
of B 2 /8 . In general, specification of B is required on all
surfaces magnetograms give photospheric B( x 1,x 2 ) what is used
on other boundaries? Strictly, NLFFF extrapolation should not be
applied to non-force-free photospheric magnetograms.
Slide 6
14 Feb 2006C4: Coronal Energy Inputs I. 2) The Magnetic Virial
Theorem (MVT) gives field energy via integration over boundary
surface. MVT assumes B is force-free, even on the boundaries - but
photosphere is forced! So MVT is best applied to chromospheric
vector magnetograms, e.g., Metcalf et al., 2003. Wheatland &
Metcalf (2005) proposed extrapolating from the forced to force-free
layers.
Slide 7
14 Feb 2006C4: Coronal Energy Inputs I. 3) Knowledge of v(x 1,x
2 ) determines energy changes for B and B (P) due to boundary
flows. Depends on photospheric (B x, B y, B z ), (v x, v y,v z ),
and (B x (P), B y (P) ). Requires vector magnetograms. Compute from
B z. How to find v?
Slide 8
14 Feb 2006C4: Coronal Energy Inputs I. 3) ILCT (Welsch et al.
2004) & other methods can determine flows from pairs of
magnetograms.
Slide 9
14 Feb 2006C4: Coronal Energy Inputs I. 3) From B(x 1,x 2,0)
and v(x 1,x 2 ), maps of the free energy flux can be computed
(Welsch et al. 2006)
Slide 10
14 Feb 2006C4: Coronal Energy Inputs I. 4) From B (P) (t 1 ), B
(P) (t 2 ), MCT calculates changes in flux ij connecting
photospheric sources i & j to estimate U (F). Each magnetogram
in a sequence is partitioned into fluxes i.
Slide 11
14 Feb 2006C4: Coronal Energy Inputs I. Role(s) of Current
Sheets 0 W fce W pot W DWDWDWDW Energy RELEASE: D W accumulates
prior to reconn burst: latency Rapidly released via local field via
local E field 4) [Lifted from Longopes talk, TRACE-RHESSI-SOHO
meeting, Dec. 2004]
Slide 12
14 Feb 2006C4: Coronal Energy Inputs I. Here are a few random
(and arguable!) thoughts that didnt fit anywhere else. Mapping free
energy using AIA data will require new techniques not so with HMI.
Techniques that can be automated would be good AIA will generate a
lot of data! AIA will tell us about non-potentiality from emergence
something HMI probably wont do so well.
Slide 13
14 Feb 2006C4: Coronal Energy Inputs I. How can we use coronal
observations to determine how much and where B differs from B (P) ?
Qualitative differences? Canfield et al. (1999) X-ray sigmoids
Schrijver, Title, & De Rosa (2005)
Slide 14
14 Feb 2006C4: Coronal Energy Inputs I. Canfield, Hudson, &
McKenzie (1999) argued that sigmoidal coronal morphologies
correlate with eruptions. They also showed that spot areas also
correlate with eruptive activity.
Slide 15
14 Feb 2006C4: Coronal Energy Inputs I. Schrijver, Title, &
DeRosa (2005) found that free energy can be detected qualitatively.
Comparisons of TRACE EUV observations with B(P) revealed
similarities & differences. similarities differences
Slide 16
14 Feb 2006C4: Coronal Energy Inputs I. How can we use coronal
observations to determine how much and where B differs from B (P) ?
Qualitative differences? Canfield et al. (1999) X-ray sigmoids
Schrijver, Title, & De Rosa (2005) Quantitative differences?
Can we infer B directly?
Slide 17
14 Feb 2006C4: Coronal Energy Inputs I. Can we infer B directly
from coronal morphology? 1.Gary & Alexander (1999) distorted of
a model B to match coronal observations. assumed an initial
topology in model B distortions were non-force-free (but perhaps
this is OK) 2.De Rosa (2004, unpublished?) investigated automated
loop identification algorithms. Punchline: This is not easy to
do!
Slide 18
14 Feb 2006C4: Coronal Energy Inputs I. How can we use coronal
observations to determine how much and where B differs from B (P) ?
Qualitative differences? Canfield et al. (1999) X-ray sigmoids
Schrijver, Title, & De Rosa (2005) Quantitative differences?
Can we infer B directly? If we cannot infer B, then what? Can we
quantify departures from B (P) ?
Slide 19
14 Feb 2006C4: Coronal Energy Inputs I. How can AIA
observations be used to quantify departures from B (P) ? Aside -
The corona exhibits ~two modes of emission: a) steady state perhaps
averaged over weak fluctuations b) highly intermittent impulsive,
stronger fluctuations What gives rise to EUV/SXR emissivity? I.)
Local emissivity steady heating? B? or ? independent of B - B (P)
(at large scales)? II.) Local emissivity intermittent magnetic
reconnection? B = B - B (P). Can we distinguish between these?
Slide 20
14 Feb 2006C4: Coronal Energy Inputs I. If steady emissivity is
a function of B (or ), then what can AIA tell us about magnetic
connections? Can Pevtsovs Law (2003), relating photospheric
magnetic flux to coronal SXR emission, be extended to EUV
observations? Does each EUV loop correspond, on average, to a
certain amount of coronal (or photospheric) flux? Study Idea:
Quantify how many EUV/SXR loops connect photospheric sources
(Voronoi regions?) of with varying flux. Applicable to MCT, which
estimates free energy by estimating flux ij linking photopheric
sources i and j.
Slide 21
14 Feb 2006C4: Coronal Energy Inputs I. From Pevtsov et al.
(2003): X-ray spectral radiance L X vs. total unsigned magnetic
flux for solar and stellar objects. Dots: Quiet Sun. Squares: X-ray
bright points. Diamonds: Solar active regions. Pluses: Solar disk
averages. Crosses: G, K, and M dwarfs. Circles: T Tauri stars.
Solid line: Power-law approximation L X 1.15 of combined data
set.
Slide 22
14 Feb 2006C4: Coronal Energy Inputs I. If emissivity B = B - B
(P), can models predict loci of reconnection-driven emission in
AIA? Several models predict (to varying degrees) reconnection
sites: Extrapolations (NLFFF & potential) MCT separators FEF
corona above free energy injection sites Longcope et al. 2005: 4 x
10 18 Mx per reconnection
Slide 23
14 Feb 2006C4: Coronal Energy Inputs I. Which observations
might we pursue? A starter list: 1.Avg. reconnected flux, , per
reconnection event? avg. reconnected flux per DN? avg. reconnected
flux per coronal loop? (vs. ?) 2.Avg. reconnection rate, / t?
3.Avg. latency time vs. spatial scale? Separatrices/ QSLs, during
emergence are thin. Does this mean reconnection happens quickly?
How about during cancellations? How about shear flows ? 4.What can
we learn from simulated emission forward models?
(Lundquist/Schrijver/Mok et al.s)
Slide 24
14 Feb 2006C4: Coronal Energy Inputs I. Emissivity appears
correlated with reconnection rate in different spectral ranges. HXR
(RHESSI)UV (TRACE) Courtesy S. Krucker Fletcher et al. 2004
Slide 25
14 Feb 2006C4: Coronal Energy Inputs I. Longcope et al. (2005)
combined TRACE data with MCT to study an emerging AR &
reconnection. In this case, flux [was] transferred as discrete
bundles of 4 x 10 18 Mx each. The sum of cross sections of all
observed loops accounts for only one-fifth of the transferred
magnetic flux predicted by the model. Could their technique be
standardized?
Slide 26
14 Feb 2006C4: Coronal Energy Inputs I. Longcope et al. (2005)
quantified EUV loops spatial and topological properties. Left:
TRACE 171 image of ARs 9570 & 9574. Right: Cross-sections of
loops intersecting slice in left image.
Slide 27
14 Feb 2006C4: Coronal Energy Inputs I. Longcope et al. (2005)
compiled statistics of EUV loops properties.
Slide 28
14 Feb 2006C4: Coronal Energy Inputs I. References Barnes et
al., 2005: Implementing a Magnetic Charge Topology Model for Solar
Active Regions, Barnes, G., Longcope, D.W., & Leka, K.D., ApJ,
v. 629, 561. Canfield et al. 1999: Sigmoidal morphology and
eruptive solar activity, Canfield, R. C., Hudson, H.S., &
McKenzie, D.E., GRL, v. 26, 627 Dmoulin & Berger, 2003:
Magnetic Energy and Helicity Fluxes at the Photospheric Level,
Dmoulin, P., and Berger, M. A. Sol. Phys., v. 215, # 2, p. 203-215.
Fletcher et al., 2003: Tracking of TRACE Ultraviolet Flare
Footpoints, Fletcher, L., Pollock, J.A.., & Potts, H.E. Sol
Phys, v. 222, 279 Gary & Alexander, 1999: Constructing the
Coronal Magnetic Field By Correlating Parameterized Magnetic Field
Lines With Observed Coronal Plasma Structures, Gary, G.A., &
Alexander, D., Sol Phys., v. 186, 123 Longcope et al., 2005:
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ApJ, v. 630, # 1, p. 596. Lundquist et al., 2005: Predicting
Coronal Emissions with Multiple Heating Rates, Lundquist, L.L.,
Fisher, G.H., Leka, K.D., Metcalf, T.R., & McTiernan, J.M., AGU
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Slide 29
14 Feb 2006C4: Coronal Energy Inputs I. Metcalf et al., 1995:
Is the solar chromospheric magnetic field force-free? Metcalf, T.
R., Jiao, L., McClymont, A. N., Canfield, R. C., Uitenbroek, H.,
ApJ, v. 439, #1, p. 474- 481. Pevtsov et al., 2003:: The
Relationship Between X-Ray Radiance and Magnetic Flux, Pevtsov,
A.A., Fisher, G.H., Acton, L.W., Longcope, D.W., Johns-Krull, C.M.,
Kankelborg, C.C., & Metcalf, T.R., ApJ, v. 598, 1387. Schrijver
et al., 2005: The Nonpotentiality of Active-Region Coronae and the
Dynamics of the Photospheric Magnetic Field, Schrijver, C. J,
DeRosa, M. L., Title, A. M., and Metcalf, T. R., ApJ, v. 628, #1,
p. 501. Schrijver et al., 2004: The Coronal Heating Mechanism as
Identified by Full-Sun Visualizations, Schrijver, C. J, Sandman, A.
W.; Aschwanden, M. J., DeRosa, M. L., ApJ, v. 615, #1, p. 512.
Welsch et al., 2004: ILCT: Recovering Photospheric Velocities from
Magnetograms by Combining the Induction Equation with Local
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and Regnier, S., ApJ, v. 610, #2, p. 1148-1156. Welsch, 2006:
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A., Roumeliotis, ApJ, v. 540, #2, p. 1150-1155. Wheatland &
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#2, 10 Jan. 2006) [on astro-ph] References, contd